Circular garden

Alice creates a circular vegetable garden. Tomatoes are planted in 1/3 of the circular garden, carrots are planted in 2/5 of the circular garden, and green peppers are planted in 1/10 of the circular garden.

What fraction represents the remaining unplanted space of the circular garden?

(Write the answer as a fraction in the lowest terms. )

Correct answer:

x =  1/6

Step-by-step explanation:

$$\begin{gathered} p=\frac{1}{3}+\frac{2}{5}+\frac{1}{10}=\frac{10}{30}+\frac{12}{30}+\frac{3}{30}=\frac{10+12+3}{30}=\frac{25}{30}=\frac{5}{6}\doteq 0.8333 \\ x=1-p=1-\frac{5}{6}=\frac{1\cdot 6}{6}-\frac{5}{6}=\frac{6}{6}-\frac{5}{6}=\frac{6-5}{6}=\frac{1}{6}=0.1667 \end{gathered}$$

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